Method and system for determining the concentration of chemical species using nmr

Abstract

Method for determining the concentrations of constituent chemical species in a mixture, including the steps of: using nuclear magnetic resonance spectroscopy, acquiring an NMR measurement for a sample of the mixture; and for each of the constituent chemical species, retrieving a reference model representative of the NMR FID signal or frequency domain spectra from a database. Each model has a number of parameters, and for at least one of the constituent chemical species, the reference model is a quantum mechanical model. The method further includes, using a computer, generating a model signal for the mixture and adjusting some or all of the model parameters to fit the model signal to the measured data; and based on the fitted model signal, calculating and displaying the concentrations of the constituent species in the sample.

1 . A method of determining the concentrations of constituent chemical species in a mixture, comprising:
 using nuclear magnetic resonance spectroscopy, acquiring an NMR measurement for a sample of the mixture;   for each of the constituent chemical species, retrieving a reference model representative of the NMR FID signal or frequency domain spectra from a database, each model having a number of parameters; wherein for at least one of the constituent chemical species, the model is a quantum mechanical model;   using a computer, generating a model signal for the mixture and adjusting some or all of the model parameters to fit the model signal to the measured data; and   based on the fitted model signal, calculating and displaying the concentrations of the constituent species in the sample.   
     
     
         2 . A method as claimed in  claim 1 , wherein the acquired NMR measurement is obtained using a benchtop-type NMR spectrometer. 
     
     
         3 . A method as claimed in  claim 1  or  2 , wherein the acquired NMR measurement is obtained using an NMR spectrometer of a type having a permanent magnet. 
     
     
         4 . A method as claimed in  claim 1 , wherein the acquired NMR measurement is obtained using an NMR spectrometer with an operating frequency of less than 100 MHz. 
     
     
         5 . A method as claimed in any preceding claim, further comprising the step of hierarchically arranging the reference models for the chemical species. 
     
     
         6 . A method as claimed in  claim 5 , wherein the step of hierarchically arranging the reference models comprises forming one or more groups containing multiple constituent species, wherein constituent species within the same group display similar responses to specific experimental conditions; and assigning one or more model parameters at the group level to reduce the overall number of parameters. 
     
     
         7 . A method as claimed in any preceding claim, wherein at least one of the constituent chemical species reference models is specified in terms of the transition peaks with parameters found by diagonalization of the spin Hamiltonian. 
     
     
         8 . A method as claimed in any preceding claim, wherein at least one of the constituent chemical species reference models is a quantum mechanical model utilising temporal propagation. 
     
     
         9 . A method as claimed in any preceding claim, wherein different types of models are used to generate the reference signals of different constituent species, the models each being selected from: a base model of spectra peaks, a quantum mechanical model utilising diagonalization, a quantum mechanical model utilising temporal propagation, and experimental data. 
     
     
         10 . A method as claimed in any preceding claim, wherein the reference signal for at least one of the chemical species is independent of the NMR instrument's field strength. 
     
     
         11 . A method as claimed in any preceding claim, wherein the mixture contains K chemical species, and the NMR signal (x) for the mixture is a superposition of the reference signals u k  of the constituent chemical species, modelled according to: 
       
         
           
             
               
                 x 
                 = 
                 
                   
                     e 
                     
                       i 
                        
                       
                           
                       
                        
                       
                         ϕ 
                         0 
                       
                     
                   
                    
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         1 
                       
                       K 
                     
                      
                     
                       
                         c 
                         k 
                       
                        
                       
                         
                           u 
                           k 
                         
                          
                         
                           ( 
                           
                             
                               θ 
                               k 
                             
                             , 
                             τ 
                           
                           ) 
                         
                       
                     
                   
                 
               
               , 
             
           
         
       
       where: θ k  represents the model parameters, τ is the ring-down delay, φ 0  is the global phase shift and c k  are intensity estimators that are proportional to the concentration of the corresponding species k. 
     
     
         12 . A method as claimed in  claim 11 , wherein the model parameters comprise one or more of: chemical shifts of the peaks, relaxation rates, peak intensities, and J-coupling constants. 
     
     
         13 . A method as claimed in any preceding claim, wherein the acquired NMR measurement is obtained using single pulse  1 H NMR 
     
     
         14 . A method as claimed in any preceding claim, the method further comprises the step of using marginal posterior distributions of the intensity estimators to analyse the uncertainties in their calculated values. 
     
     
         15 . A method as claimed in  claim 14 , further comprising the step of using an MCMC algorithm to sample the posterior distribution of the fitted model to estimate the uncertainty of the model parameters. 
     
     
         16 . A method as claimed in  claim 14  or  15 , wherein, along with the step of displaying the concentrations of the constituent species in the sample, the confidence or credible intervals relating to the concentrations are displayed. 
     
     
         17 . A method as claimed in  claim 16  wherein the confidence or credible intervals are calculated using a robust variance estimator taking into account the residual signal between the model signal and the NMR measurements. 
     
     
         18 . A method as claimed in any preceding claim, wherein the step of fitting the model signal, or calculating the concentrations of the constituent species further comprises the step of performing line shape correction. 
     
     
         19 . A method as claimed in any preceding claim, wherein the step of fitting the model signal, or calculating the concentrations of the constituent species comprises utilising a generalized least squares (GLS) estimator. 
     
     
         20 . A method as claimed in  claim 19 , wherein the generalized least squares (GLS) estimator treats possible model misspecification as additional non-isotropic noise. 
     
     
         21 . A method as claimed in  claim 19  or  20 , wherein, in the frequency domain, the variance of the noise assumed to be proportional to the absolute value of the derivative of the modelled NMR spectra. 
     
     
         22 . A method as claimed in any preceding claim, wherein the mixture comprises sugars. 
     
     
         23 . A method as claimed in  claim 22 , wherein the chemical species comprise one or more of glucose, fructose and sucrose. 
     
     
         24 . A method as claimed in  claim 22  or  23 , wherein the mixture is a fruit juice. 
     
     
         25 . A method as claimed in any one of  claims 1  to  21 , wherein the chemical species comprise one or more alcohols. 
     
     
         26 . A system for determining the concentrations of constituent chemical species in a mixture, comprising:
 a nuclear magnetic resonance (NMR) spectrometer, for acquiring an NMR measurement of a sample of the mixture;   a computer storage media comprising a database of NMR FID signal or frequency domain spectra reference models for each constituent species, each model having a number of parameters; wherein for at least one of the constituent chemical species, the model is a quantum mechanical model;   a model signal generator configured to generate a model signal for the mixture and adjust some or all of the model parameters to fit the model signal to the measured data, and thereby calculate the concentrations of each of the constituent species in the sample; and   a user interface for receiving input commands from a user and for displaying the calculated concentrations of each of the constituent species.   
     
     
         27 . A system as claimed in  claim 26 , wherein the model generator comprises means for combining the reference models for each constituent species to generate the model signal. 
     
     
         28 . A system as claimed in  claim 26  or  27 , wherein the NMR spectrometer is a benchtop-type spectrometer. 
     
     
         29 . A system as claimed in any one of  claims 26  to  28 , wherein the NMR spectrometer of a type having a permanent magnet. 
     
     
         30 . A system as claimed in any one of  claims 26  to  29 , wherein the NMR spectrometer operates at less than 100 MHz. 
     
     
         31 . A system as claimed in any one of  claims 26  to  30 , comprising means for hierarchically arranging the chemical species and their respective reference models. 
     
     
         32 . A system as claimed in any one of  claims 26  to  31 , wherein at least one of the constituent chemical species reference models in the database is specified in terms of the transition peaks with parameters found by diagonalization of the spin Hamiltonian. 
     
     
         33 . A method as claimed in any one of  claims 26  to  32 , wherein at least one of the constituent chemical species reference models in the database is a quantum mechanical model utilising temporal propagation. 
     
     
         34 . A system as claimed in any one of  claims 26  to  33 , wherein the database comprises different types of reference models for different constituent species, the model types being selected from: a base model of spectra peaks, a quantum mechanical model utilising diagonalization, a quantum mechanical model utilising temporal propagation, and experimental data. 
     
     
         35 . A system as claimed in any one of  claims 26  to  34 , wherein at least one of the reference models in the database is independent of the field strength of the NMR spectrometer. 
     
     
         36 . A system as claimed in any one of  claims 26  to  35 , wherein the model signal generator combines the reference signals u k  for a mixture containing K chemical species using superposition, and generates the NMR signal (x) for the mixture according to: 
       
         
           
             
               
                 x 
                 = 
                 
                   
                     e 
                     
                       i 
                        
                       
                           
                       
                        
                       
                         ϕ 
                         0 
                       
                     
                   
                    
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         1 
                       
                       K 
                     
                      
                     
                       
                         c 
                         k 
                       
                        
                       
                         
                           u 
                           k 
                         
                          
                         
                           ( 
                           
                             
                               θ 
                               k 
                             
                             , 
                             τ 
                           
                           ) 
                         
                       
                     
                   
                 
               
               , 
             
           
         
       
       where: θ k  represents the model parameters, τ is the ringdown delay, φ 0  is the global phase shift and c k  are intensity estimators that are proportional to the concentration of the corresponding species k. 
     
     
         37 . A system as claimed in  claim 36 , wherein the model parameters comprise one or more of: chemical shifts of the peaks, relaxation rates, peak intensities, and J-coupling constants. 
     
     
         38 . A system as claimed in any one of  claims 26  to  37 , further comprising the step of using an MCMC algorithm to sample to posterior distribution of the fitted model to estimate the uncertainty of the model parameters. 
     
     
         39 . A system as claimed in any one of  claims 26  to  38 , along with the step of displaying the concentrations of the constituent species in the sample, the confidence intervals relating to the concentrations are displayed. 
     
     
         40 . A non-transient computer readable medium containing program instructions for causing a computer to:
 upon receiving an NMR measurement for a sample of a mixture of a number of known constituent chemical species, retrieve a reference model representative of the NMR FID signal or frequency domain spectra for each specie from a database, each model having a number of parameters; at least one of the retrieved reference models being a quantum mechanical model;   generate a computer readable model signal for the mixture and adjust some or all of the model parameters to fit the model signal to the measured data; and based on the fitted model signal, calculate and display the concentrations of the constituent species in the sample.